Outsourcing enterprise IT service management is an increasingly challenging business. On one hand, service providers must deliver with respect to customer expectations of service quality and innovation. On the other hand, they must continuously seek competitive reductions in the costs of service delivery and management. These targets can be achieved with integration of innovative service management tools, automation, and advanced analytics. In this paper, we focus on service analytics, the subset of analytics problems and solutions concerning specific service delivery and management performance and cost optimization. The paper reviews various service analytics methods and technologies that have been developed and applied to enhance IT service management. We use our industrial experience to highlight the challenges faced in the development and adoption of service analytics, and we discuss open problems.